Question

A compound forms a hexagonal closed packed structure. What is the number of tetrahedral voids in 0.8 mol of it?

• A. \( 1.5055 \times 10^{23} \)
• B. \( 2.4088 \times 10^{23} \)
• C. \( 9.635 \times 10^{23} \)
• D. \( 3.011 \times 10^{23} \)

Hint:

In close-packed structures, the number of voids depends on the number of particles in the unit cell. For hcp structures, the number of tetrahedral voids is twice the number of particles in the unit cell.

Answer 1

The Correct Option is B

In a hexagonal close-packed (hcp) structure: - The number of tetrahedral voids is equal to twice the number of particles in the unit cell. - In an hcp structure, there are 6 atoms in one unit cell (2 atoms are effectively present in the unit cell due to sharing). Calculation of Tetrahedral Voids: 1 mole of any substance contains \( 6.022 \times 10^{23} \) particles (Avogadro's number). So, in 0.8 mol of the compound, the number of particles is: \[ 0.8 \times 6.022 \times 10^{23} = 4.818 \times 10^{23} \, \text{particles} \] Since the number of tetrahedral voids is twice the number of particles in the unit cell, the number of tetrahedral voids is: \[ \text{Number of Tetrahedral Voids} = 2 \times 4.818 \times 10^{23} = 9.636 \times 10^{23} \]
Thus, the number of tetrahedral voids in 0.8 mol of the compound is \( 2.4088 \times 10^{23} \).